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Learning path · 9 steps

3D math foundations

The vector, angle and transform toolkit behind every 3D game. Start here before physics, animation or rendering.

Start: Vector Basics
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  1. Mathematicscore1. Vector BasicsPositions, directions and lengths: the alphabet of 3D code.
  2. Mathematicscore2. Dot and Cross ProductMeasure alignment and build perpendiculars, normals and torque.
  3. Mathematicscore3. Trigonometry for GamesTurn angles into directions and back with sin, cos and atan2.
  4. Mathematicscore4. Transforms and MatricesMove, rotate and scale in one matrix, in the right order.
  5. Mathematicscore5. Local vs World SpaceParent/child hierarchies and converting points between spaces.
  6. Mathematicscommon6. Euler Angles and Gimbal LockHuman-friendly rotations and the gimbal lock they hide.
  7. Mathematicscore7. QuaternionsRobust rotation storage and smooth slerp.
  8. Mathematicscore8. Lerp and SmoothstepBlend any value smoothly and frame-rate independently.
  9. Mathematicscommon9. Bézier CurvesPaths for cameras, projectiles and UI motion.